Hybrid control of Hopf bifurcation in a fractional order small-world network model

In this paper, a hybrid control strategy is applied to control the Hopf bifurcation in a fractional order small-world network model. By choosing time-delay as a bifurcation parameter and analyzing the associated characteristic equation, we prove that the model exhibits Hopf bifurcation when time delay passes through a critical value. In order to control the undesirable Hopf bifurcation, a hybrid control strategy is proposed. By adjusting the control parameters of the strategy, it shows that the onset of Hopf bifurcation has been postponed without changing the original equilibrium point of the system. Finally, a numerical simulation is presented to verify the theoretical results.